You don't need to know this, but...
The hydrated lime you're spreading on to your walls is going to gradually turn into limestone. There's something in nature called "the lime cycle" whereby limestone that comes from marine reefs that formed millions of years ago can be heated to form "hot lime" or "quick lime". That hot lime or Calcium oxide can then be mixed with water to form the hydrated lime that you're mixing with gypsum (Plaster of Paris) and sand to form your base coat plaster.
But, over the next several years, that hydrated lime (Ca(OH2)) will react with the carbon dioxide in the air to form calcium carbonate (Ca(CO3)), or the primary constituent in what we call "limestone". The purer the calcium carbonate, the whiter it is, and limestone that is quarried will typically be at least 90 percent calcium carbonate.
The above is important because until the hydrated lime in your plaster patches transforms into limestone, it's going to be highly alkaline because of all those -OH groups in the hydrated lime. The high alkalinity of that lime will cause any oil based primer or paint to basically turn into soap if you paint it on your base coat plaster. If you're planning to paint over your base coat plaster within the next couple of years, then you should buy a latex primer made especially for fresh concrete (called a "concrete primer".)
What you might want to do instead is skim coat over your base coat plaster with drywall joint compound, sand that smooth, and prime and paint with whatever primer and paint you like over that. Drywall joint compound consists of gypsum, and so it's neither alkaline nor acidic.
PS: The reason why the cement based grout used in bathroom ceramic tiling won't mildew in the first year or two is because the grout is a cement based product made with lime. Until the lime in that grout transforms into limestone, then the grout will be too alkaline for mildew to grow on it. This is why ceramic tiling contractors can guarantee their work for one year. They know that it takes about two years for the lime to transform into limestone, and it's only then that mildew will begin to grow on the grout.